'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Which means for our asset as example:- Looking at the total return of 221.2% in the last 5 years of ProShares Ultra Dow30, we see it is relatively higher, thus better in comparison to the benchmark SPY (122.7%)
- During the last 3 years, the total return, or increase in value is 65.4%, which is larger, thus better than the value of 65.3% from the benchmark.

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Which means for our asset as example:- The annual return (CAGR) over 5 years of ProShares Ultra Dow30 is 26.3%, which is greater, thus better compared to the benchmark SPY (17.4%) in the same period.
- During the last 3 years, the annual performance (CAGR) is 18.3%, which is higher, thus better than the value of 18.2% from the benchmark.

'Volatility is a rate at which the price of a security increases or decreases for a given set of returns. Volatility is measured by calculating the standard deviation of the annualized returns over a given period of time. It shows the range to which the price of a security may increase or decrease. Volatility measures the risk of a security. It is used in option pricing formula to gauge the fluctuations in the returns of the underlying assets. Volatility indicates the pricing behavior of the security and helps estimate the fluctuations that may happen in a short period of time.'

Which means for our asset as example:- The historical 30 days volatility over 5 years of ProShares Ultra Dow30 is 39.2%, which is larger, thus worse compared to the benchmark SPY (18.7%) in the same period.
- Looking at 30 days standard deviation in of 47.3% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (22.5%).

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk in our definition is the semi-deviation, that is the standard deviation of all negative returns.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (13.6%) in the period of the last 5 years, the downside deviation of 28.3% of ProShares Ultra Dow30 is larger, thus worse.
- During the last 3 years, the downside volatility is 34.2%, which is greater, thus worse than the value of 16.3% from the benchmark.

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Which means for our asset as example:- The Sharpe Ratio over 5 years of ProShares Ultra Dow30 is 0.61, which is lower, thus worse compared to the benchmark SPY (0.8) in the same period.
- Compared with SPY (0.7) in the period of the last 3 years, the Sharpe Ratio of 0.33 is lower, thus worse.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (1.1) in the period of the last 5 years, the excess return divided by the downside deviation of 0.84 of ProShares Ultra Dow30 is lower, thus worse.
- Compared with SPY (0.96) in the period of the last 3 years, the downside risk / excess return profile of 0.46 is lower, thus worse.

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Which means for our asset as example:- Compared with the benchmark SPY (5.58 ) in the period of the last 5 years, the Ulcer Index of 14 of ProShares Ultra Dow30 is higher, thus worse.
- Compared with SPY (6.83 ) in the period of the last 3 years, the Downside risk index of 17 is larger, thus worse.

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

Which means for our asset as example:- Looking at the maximum drop from peak to valley of -63.1 days in the last 5 years of ProShares Ultra Dow30, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum drop from peak to valley is -63.1 days, which is lower, thus worse than the value of -33.7 days from the benchmark.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Which means for our asset as example:- Looking at the maximum days under water of 248 days in the last 5 years of ProShares Ultra Dow30, we see it is relatively greater, thus worse in comparison to the benchmark SPY (139 days)
- During the last 3 years, the maximum time in days below previous high water mark is 248 days, which is larger, thus worse than the value of 139 days from the benchmark.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (33 days) in the period of the last 5 years, the average days under water of 66 days of ProShares Ultra Dow30 is larger, thus worse.
- During the last 3 years, the average days under water is 78 days, which is greater, thus worse than the value of 35 days from the benchmark.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares Ultra Dow30 are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.